Question: Solve for $x$ and $y$ using elimination. ${-2x-2y = -12}$ ${-3x+2y = -8}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2y$ and $2y$ cancel out. $-5x = -20$ $\dfrac{-5x}{{-5}} = \dfrac{-20}{{-5}}$ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $\thinspace {-2x-2y = -12}\thinspace$ to find $y$ ${-2}{(4)}{ - 2y = -12}$ $-8-2y = -12$ $-8{+8} - 2y = -12{+8}$ $-2y = -4$ $\dfrac{-2y}{{-2}} = \dfrac{-4}{{-2}}$ ${y = 2}$ You can also plug ${x = 4}$ into $\thinspace {-3x+2y = -8}\thinspace$ and get the same answer for $y$ : ${-3}{(4)}{ + 2y = -8}$ ${y = 2}$